Model for Vortex Pinning in a Two-Dimensional Inhomogeneous d-wave Superconductor

TL;DR

This paper presents a model for vortex pinning in inhomogeneous 2D d-wave superconductors, showing vortices prefer large-gap regions and reproducing key features of scanning tunneling spectroscopy observations.

Contribution

The study introduces a novel model linking inhomogeneity in T_{c0} and (0) to vortex pinning behavior, aligning theoretical results with experimental spectroscopic data.

Findings

Vortices tend to pin where the superconducting gap is large.

The local density of states near vortices matches experimental spectra.

The model explains absence of zero-energy peaks near vortex cores.

Abstract

We study a model for the pinning of vortices in a two-dimensional, inhomogeneous, Type-II superconductor in its mixed state. The model is based on a Ginzburg-Landau (GL) free energy functional whose coefficients are determined by the mean-field transition temperature T_{c0} and the zero-temperature penetration depth \lambda(0). We find that if (i) T_{c0} and \lambda(0) are functions of position, and (ii) \lambda^2(0) is proportional to T_{c0}^y, with y greater than 0, then the vortices tend to be pinned where T_{c0}, and hence the magnitude of the superconducting order parameter \Delta, are large. This behavior is in contrast to the usual picture of pinning in Type-II superconductors, where pinning occurs in the small-gap regions. We also compute the local density of states of a model BCS Hamiltonian with d-wave symmetry, in which the pairing field is obtained from Monte Carlo simulations of a GL free energy. Several features observed in scanning tunneling spectroscopy measurements on YBa_2Cu_3O_{6+x} and Bi_2Sr_2CaCu_2O_{8+x} are well reproduced by our model: far from the cores, the local density of states spectrum has a small gap and sharp coherence peaks, while near the cores it has a larger gap with low, broad peaks. Additionally, also in agreement with experiment, the spectrum near the core does not exhibit a zero-energy peak which is, however, observed in other theoretical studies.